Graph Denoising with Framelet Regularizer

TL;DR

This paper introduces a novel graph denoising method using framelet regularizers that enhances robustness to noise in both features and structure, outperforming existing graph convolution techniques.

Contribution

It proposes a new regularization approach tailored for noisy graph data, solved efficiently with ADMM, enabling multi-layer graph neural networks without over-smoothing.

Findings

Significantly improved performance on noisy graphs

Effective denoising of both features and structure

Convergence guarantees for the proposed method

Abstract

As graph data collected from the real world is merely noise-free, a practical representation of graphs should be robust to noise. Existing research usually focuses on feature smoothing but leaves the geometric structure untouched. Furthermore, most work takes L2-norm that pursues a global smoothness, which limits the expressivity of graph neural networks. This paper tailors regularizers for graph data in terms of both feature and structure noises, where the objective function is efficiently solved with the alternating direction method of multipliers (ADMM). The proposed scheme allows to take multiple layers without the concern of over-smoothing, and it guarantees convergence to the optimal solutions. Empirical study proves that our model achieves significantly better performance compared with popular graph convolutions even when the graph is heavily contaminated.